Solve for $x$ and $y$ by deriving an expression for $x$ from the second equation, and substituting it back into the first equation. $\begin{align*}-5x+6y &= 9 \\ 5x-2y &= -6\end{align*}$
Answer: Begin by moving the $y$ -term in the second equation to the right side of the equation. $5x = 2y-6$ Divide both sides by $5$ to isolate $x$ $x = {\dfrac{2}{5}y - \dfrac{6}{5}}$ Substitute this expression for $x$ in the first equation. $-5({\dfrac{2}{5}y - \dfrac{6}{5}}) + 6y = 9$ $-2y + 6 + 6y = 9$ Simplify by combining terms, then solve for $y$ $4y + 6 = 9$ $4y = 3$ $y = \dfrac{3}{4}$ Substitute $\dfrac{3}{4}$ for $y$ in the top equation. $-5x+6( \dfrac{3}{4}) = 9$ $-5x+\dfrac{9}{2} = 9$ $-5x = \dfrac{9}{2}$ $x = -\dfrac{9}{10}$ The solution is $\enspace x = -\dfrac{9}{10}, \enspace y = \dfrac{3}{4}$.